Cristiano Ronaldo opened the scoring for Madrid as he chipped home Mesut Ozil's through ball after just 9 minutes.
Karim Benzema silenced his critics with a well taken effort at the half-hour mark.
Wesley Sneijder was a bitter disappointment for the Turkish side and was substituted at half-time.
The tie was virtually killed off 17 minutes from time after substitute Gonzalo Higuain headed home Xabi Alonso's free-kick.
It was a night of contrasting fortunes for Ronaldo and Didier Drogba, with the Ivory Coast striker unable to influence the game.
Borussia Dortmund were left to rue a host of missed chances as the quarter-final first leg against Malaga at La Rosaleda ended in a 0-0 draw.
Dortmund remain the only unbeaten team in the Champions League this season, while Malaga extended their unbeaten home record in Europe to 14 games.
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